Question

if a line intersects two concentric circles with centre O A,B,C and D,prove that AB equal to CD​

Answer 1

Answer:

We know that,

OA=OD

OA=OD

and

OB=OC

OB=OC

.

They are radius of respective circles.

In

\Delta OBC

ΔOBC

, we know that

OB=OC

OB=OC

, so

\angle OBC = \angle OCB

∠OBC=∠OCB

\therefore \angle OCD= \angle OBA

∴∠OCD=∠OBA

In

\Delta OAD

ΔOAD

, we know that

OA=OD

OA=OD

, so

\angle OAD = \angle ODA

∠OAD=∠ODA

Since,

\angle OCD = \angle OBA

∠OCD=∠OBA

and

\angle OAD = \angle ODA

∠OAD=∠ODA

, we get

\angle AOB

∠AOB

in

\Delta OAB

ΔOAB

is equal to

\angle COD

∠COD

in

\Delta OCD

ΔOCD

.

\therefore

∴

From

SAS

SAS

congruency, we can say that

\Delta OAB

ΔOAB

and

\Delta OCD

ΔOCD

are congruent.

So,

AB=CD

AB=CD

.

Answer 2

Answer:

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